Digital compensator for a non-linear system

Abstract

A pre-distorter that both accurately compensates for the non-linearities of a radio frequency transmit chain, and that imposes as few computation requirements in terms of arithmetic operations, uses a diverse set of real-valued signals that are derived from the input signal. The derived real signals are passed through configurable non-linear transformations, which may be adapted during operation, and which may be efficiently, implemented using lookup tables. The outputs of the non-linear transformations serve as gain terms for a set of complex signals, which are functions of the input, and which are summed to compute the pre-distorted signal. A small set of the complex signals and derived real signals may be selected for a particular system to match the classes of non-linearities exhibited by the system, thereby providing further computational savings, and reducing complexity of adapting the pre-distortion through adapting of the non-linear transformations.

What is claimed is: 
     
       1. A method of signal predistortion for linearizing a non-linear circuit, the method comprising:
 processing an input signal (u) to produce a plurality of transformed signals (w); 
 determining a plurality of phase-invariant derived signals (r), each derived signal (r j ) of the plurality of derived signals being equal to a respective non-linear function of one or more of the transformed signals, at least some of the derived signals being equal to respective functions of different one or more of the transformed signals; 
 transforming each derived signal (r j ) of the plurality of phase-invariant derived signals according to a parametric non-linear transformation to produce a time-varying gain component (g i ) of a plurality of gain components (g); 
 forming a distortion term by accumulating a plurality of terms, each term being a product of a respective transformed signal of the plurality of transformed signals and a respective time-varying gain, the time-varying gain being a function (Φ) of a one or more of the phase-invariant derived signals, the function of the one or more of the phase-invariant derived signals being decomposable into a combination of one or more parametric functions (ϕ) of a corresponding single one of the phase invariant derived signals (r j ) yielding a corresponding one of the time-varying gain components (g i ); and 
 providing an output signal (v) determined from the distortion term for application to the non-linear circuit. 
 
     
     
       2. The method of  claim 1  where the non-linear circuit comprises a radio-frequency section including a radio-frequency modulator configured to modulate the output signal to a carrier frequency to form a modulated signal and an amplifier for amplifying the modulated signal. 
     
     
       3. The method of  claim 1  wherein processing the input signal (u) to produce the plurality of transformed signals (w) includes forming at least one of the transformed signals as a linear combination of the input signal (u) and one or more delayed versions of the input signal. 
     
     
       4. The method of  claim 3  wherein forming at least one of the transformed signals as a linear combination includes forming a linear combination with at least one imaginary or complex multiple input signal or a delayed version of the input signal. 
     
     
       5. The method of  claim 4  wherein forming at least one of the transformed signals, w k  to be a multiple of D α w a +j d w b , where w a  and w b  are other of the transformed signals, and D α  represents a delay by α, and d is an integer between 0 and 3. 
     
     
       6. The method of  claim 5  wherein forming the at least one of the transformed signals includes time filtering the input signal to form said transformed signal. 
     
     
       7. The method of  claim 1  wherein determining a plurality of phase-invariant derived signals (r) comprises determining real-valued derived signals including processing the transformed signals (w) to produce a plurality of phase-invariant derived signals (r). 
     
     
       8. The method of  claim 7  wherein processing the transformed signals (w) to produce a plurality of phase-invariant derived signals includes for at least one derived signal (r p ) computing said derived signal by first computing a phase-invariant non-linear function of one of the transformed signals (w k ) to produce a first derived signal, and then computing a linear combination of the first derived signal and delayed versions of the first derived signal to determine the at least one derived signal. 
     
     
       9. The method of  claim 8  wherein computing the linear combination of the first derived signal and delayed versions of the first derived signal comprises time filtering the first derived signal. 
     
     
       10. The method of  claim 7  wherein processing the transformed signals (w) to produce a plurality of phase-invariant derived signals includes computing a first signal as a phase-invariant non-linear function of a first signal of the transformed signals, and computing a second signal as a phase-invariant non-linear function of a second of the transformed signals, and then computing a combination of the first signal and the second signal to form at least one of the phase-invariant derived signals. 
     
     
       11. The method of  claim 7  wherein processing the transformed signals (w) to produce a plurality of phase-invariant derived signals includes computing a derived signal r k [t] using at least one of the following transformations:
     r   k [ t ]=| w   a [ t ]| α , 
 
       where α>0 for a transformed signal w a  [t];
     r   k [ t ]=0.5(1 −θ+r   a [ t −α]+θ r   b [ t ]),
 
 
       where θ∈{1,−1}, a,b∈{1, . . . , k−1}, and α is an integer and r a [t] and r b [t] are other of the derived signals;
     r   k [ t ]= r   a [ t −α] r   b [ t ],
 
 
       where a,b∈{1, . . . , k−1} and α is an integer and r a [t] and r b [t] are other of the derived signals; and
     r   k [ t ]= r   k [ t −1]+2 −d ( r   a [ t ]− r   k [ t −1]),
 
 
       where a∈{1, . . . , k−1} and d is an integer d>0. 
     
     
       12. The method of  claim 1  further comprising transforming a first derived signal (r j ) of the plurality of phase-invariant derived signals according to one or more different parametric non-linear transformation to produce a corresponding time-varying gain components. 
     
     
       13. The method of  claim 12  wherein the one or more different parametric non-linear transformations comprises multiple different non-linear transformations producing corresponding time-varying gain components. 
     
     
       14. The method of  claim 13  wherein each of the corresponding time-varying gain components forms a part of a different term of the plurality of terms of the distortion term. 
     
     
       15. The method of  claim 1  wherein forming the distortion term comprises forming a first sum of products, each term in the first sum being a product of a delayed version of the transformed signal and a second sum of a corresponding subset of the gain components. 
     
     
       16. The method of  claim 15  wherein the distortion term δ[t] has a form 
       
         
           
             
               
                 δ 
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                   [ 
                   t 
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               = 
               
                 
                   ∑ 
                   k 
                   
                       
                   
                 
                 ⁢ 
                 
                   
                     
                       w 
                       
                         a 
                         k 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         t 
                         - 
                         
                           d 
                           k 
                         
                       
                       ] 
                     
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         i 
                         ∈ 
                         
                           Λ 
                           k 
                         
                       
                       
                           
                       
                     
                     ⁢ 
                     
                       
                         g 
                         i 
                       
                       ⁡ 
                       
                         [ 
                         t 
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         wherein for each term indexed by k, a k  selects the transformed signal, d k  determines the delay of said transformed signal, and Λ k  determines the subset of the gain components. 
       
     
     
       17. The method of  claim 1  wherein transforming a first derived signal of the plurality of derived signals according to a parametric non-linear transformation comprises performing a table lookup in a data table corresponding to said transformation according to the first derived signal to determine a result of the transforming. 
     
     
       18. The method of  claim 17  wherein the parametric non-linear transformation comprises a plurality of segments, each segment corresponding to a different range of values of the first derived signal, and wherein transforming the first derived signal according to the parametric non-linear transformation comprises determining a segment of the parametric non-linear transformation from the first derived signal and accessing data from the data table corresponding to a said segment. 
     
     
       19. The method of  claim 18  wherein the parametric non-linear transformation comprises a piecewise linear or a piecewise constant transformation, and the data from the data table corresponding to said segment characterizes endpoints of said segment. 
     
     
       20. The method of  claim 19  wherein the non-linear transformation comprises a piecewise linear transformation, and transforming the first derived signal comprises interpolating a value on a linear segment of said transformation. 
     
     
       21. The method of  claim 1  further comprising adapting configuration parameters of the parametric non-linear transformation according to sensed output of the non-linear circuit. 
     
     
       22. The method of  claim 21  further comprising acquiring a sensing signal (y) dependent on an output of the non-linear circuit, and wherein adapting the configuration parameters includes adjusting said parameters according to a relationship of the sensing signal (y) and at least one of the input signal (u) and the output signal (v). 
     
     
       23. The method of  claim 22  wherein adjusting said parameters includes reducing a mean squared value of a signal computed from the sensing signal (y) and at least one of the input signal (u) and the output signal (v) according to said parameters. 
     
     
       24. The method of  claim 23  wherein reducing the mean squared value includes applying a stochastic gradient procedure to incrementally update the configuration parameters. 
     
     
       25. The method of  claim 23  wherein reducing the mean squared value includes processing a time interval of the sensing signal (y) and a corresponding time interval of at least one of the input signal (u) and the output signal (v). 
     
     
       26. The method of  claim 25  comprising performing a matrix inverse of a Gramian matrix determined from the time interval of the sensing signal and a corresponding time interval of at least one of the input signal (u) and the output signal (v). 
     
     
       27. The method of  claim 26  further comprising forming the Gramian matrix as a time average Gramian. 
     
     
       28. The method of  claim 21  wherein transforming a first derived signal of the plurality of derived signals according to a parametric non-linear transformation comprises performing a table lookup in a data table corresponding to said transformation according to the first derived signal to determine a result of the transforming, and wherein adapting the configuration parameters comprises updating values in the data table. 
     
     
       29. The method of  claim 28  wherein the parametric non-linear transformation comprises a greater number of piecewise linear segments than adjustable parameters characterizing said transformation. 
     
     
       30. The method of  claim 29  wherein the non-linear transformation represents a function that is a sum of scaled kernels, a magnitude scaling each kernel being determined by a different one of the adjustable parameters characterizing said transformation. 
     
     
       31. The method of  claim 30  wherein each kernel comprises a piecewise linear function. 
     
     
       32. The method of  claim 30  wherein each kernel is zero for at least some range of values of the derived signal. 
     
     
       33. The method of  claim 1  wherein the non-linear functions of the input signal (u) comprises at least one function of a form
     u [ n −τ]| u [ n −τ]| p  
 
 for a delay τ and an integer power p or
   Π j=1 . . . p   u [ n−τ   j ]Π j=p+1 . . . 2p-1   u [ n−τ   j ]*
 
 
 for a set for integer delays τ 1  to Σ 2p-1 , where * indicates a complex conjugate operation. 
 
     
     
       34. A method of signal predistortion for linearizing a non-linear circuit comprising a radio-frequency section including a radio-frequency modulator configured to modulate an output signal to a carrier frequency to form a modulated signal and an amplifier for amplifying the modulated signal, the method comprising:
 processing an input signal (u) to produce a plurality of transformed signals (w), the input signal (u) comprising quadrature components of a baseband signal for transmission via the radio-frequency section, and the plurality of transformed signals (w) comprising complex-valued signals; 
 determining a plurality of phase-invariant real-valued derived signals (r), each derived signal (r j ) of the plurality of derived signals being equal to a respective non-linear function of one or more of the transformed signals, at least some of the derived signals being equal to respective functions of different one or more of the transformed signals; 
 transforming each derived signal (r j ) of the plurality of phase-invariant derived signals according to a parametric non-linear transformation to produce a time-varying gain component (g i ) of a plurality of gain components (g), including transforming a first derived signal (r j ) of the plurality of phase-invariant derived signals according to one or more different parametric non-linear transformation to produce corresponding time-varying gain components, wherein transforming the first derived signal of the plurality of derived signals according to a parametric non-linear transformation comprises performing a table lookup in a data table corresponding to said transformation according to the first derived signal to determine a result of the transforming, and wherein the parametric non-linear transformation comprises a piecewise linear transformation, and the data from the data table corresponding to said segment characterizes endpoints of said segment and transforming the first derived signal comprises interpolating a value on a linear segment of said transformation; 
 forming a distortion term by accumulating a plurality of terms, each term being a product of a transformed signal of the plurality of transformed signals and a time-varying gain, the time-varying gain being a function (Φ) of a one or more of the phase-invariant derived signals, the function of the one or more of the phase-invariant derived signals being decomposable into a combination of one or more parametric functions (ϕ) of a corresponding single one of the phase invariant derived signals (r j ) yielding a corresponding one of the time-varying gain components (g i ); 
 providing an output signal (v) determined from the distortion term for application to the non-linear circuit; and 
 adapting configuration parameters of the parametric non-linear transformation according to sensed output of the non-linear circuit, including updating values in the data table. 
 
     
     
       35. A digital predistorter circuit comprising:
 an input port for receiving an input signal (u); 
 an output port for providing an output signal (v); 
 storage for values of a plurality of configuration parameters (x); 
 wherein the circuit is configured to perform operations comprising: 
 receiving the input signal (u) via the input port; 
 processing the input signal (u) to produce a plurality of transformed signals (w); 
 determining a plurality of phase-invariant derived signals (r), each derived signal (r j ) of the plurality of derived signals being equal to a respective non-linear function of one or more of the transformed signals, at least some of the derived signals being equal to respective functions of different one or more of the transformed signals; 
 transforming each derived signal (r j ) of the plurality of phase-invariant derived signals according to a parametric non-linear transformation to produce a time-varying gain component (g i ) of a plurality of gain components (g); 
 forming a distortion term by accumulating a plurality of terms, each term being a product of a transformed signal of the plurality of transformed signals and a time-varying gain, the time-varying gain being a function (Φ) of a one or more of the phase-invariant derived signals, the function of the one or more of the phase-invariant derived signals being decomposable into a combination of one or more parametric functions (ϕ) of a corresponding single one of the phase invariant derived signals (r j ) yielding a corresponding one of the time-varying gain components (g i ); and 
 providing the output signal (v) determined from the distortion term via the output port. 
 
     
     
       36. A non-transitory machine-readable medium comprising a design structure, said design structure comprising elements that, when processed in a computer-aided design system, generates a machine-executable representation of the digital predistortion circuit of  claim 35 .